# 7.35: Untitled Page 180

## Chapter 7

and choose a value for the parameter, q , that provides for a severely damped convergence. The results are shown in Table 7.8b where we see that the iterative procedure converges rapidly to the value given by x  ( M

)

  0 . 6108

(42)

C2H4 5

Use of this result in Eq. 20 allows us to determine the fraction of Stream #4

that is purged and this fraction is given by

( M

) CY

C H

5 

  1 

(43)

2 4 C

 0 2874

.

1

which is identical to that obtained in Example 7.6.

Table 7.8b. Iterative Values for Dimensionless Flow Rate

(Wegstein’s Method)

i

q

xi

xi+1

0

0.9950

0.7500

0.4070

1

0.9950

0.4070

0.5265

2

0.9950

0.5265

0.5938

3

0.9950

0.5938

0.6109

4

0.9950

0.6109

0.6108

5

0.9950

0.6108

0.6108

7.5 Problems

Note: Problems marked with the symbol  will be difficult to solve without the use of computer software.

Section 7.1

7‐1. In the production of formaldehyde ( CH O ) by catalytic oxidation of 2

methanol ( CH OH ) an equi‐molar mixture of methanol and air (21% oxygen 3

and 79% nitrogen) is sent to a catalytic reactor. The reaction is catalyzed by finely divided silver supported on alumina as suggested in Figure 7.1 where we Material Balances for Complex Systems

337

Figure 7.1. Production of formaldehyde

have indicated that carbon dioxide ( CO ) is produced as an undesirable 2

product. The conversion for methanol ( CH OH ) is given by 3

 RCH OH

C  Conversion of CH OH 

 0 2

. 0

3

3

M CH3OH1

and the selectivity for formaldehyde / carbon dioxide is given by RCH O

2

S  Selectivity of CH O/CO

 8 . 5

2

2

RCO2

In this problem you are asked to determine the mole fraction of all components in the Stream #2 leaving the reactor.

7‐2. Use the pivot theorem (Sec. 6.4) with Eq. 6 of Example 7.1 to develop a solution for R

and R

using ethylene ( C H ) , methane ( CH ) and

H2

C2H6

2

4

4

propylene ( C H ) as the pivot species. Compare your solution with Eq. 7 and 3

6

Eq. 8 of Example 7.1. In order to use ethylene ( C H ) , ethane ( C H ) , and 2

4

2

6

propylene ( C H ) as the pivot species, one needs to use a column/row 3

6

interchange (see Sec. 6.2.5) with Eq. 6 of Example 7.1. Carry out the appropriate column /row interchange and the necessary elementary row operations and use the pivot theorem to develop a solution for R

and

H

R

.

CH

2

4

7‐3. An industrial process for making acetic anhydride utilizes the highly unsaturated and reactive ketene ( CH CO ) that is also an important intermediate 2

in other chemical processes. The pyrolysis of acetone ( CH COCH ) in an 3

3

externally heated empty tube produces ketene ( CH CO ) and methane ( CH ) .

2

4

This is illustrated in Figure 7.3 where we have indicated that some of the ketene   338